Some characteristics of primes within modular rings

J. V. Leyendekkers and A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 9, 2003, Number 3, Pages 49–58
Full paper (PDF, 3999 Kb)

Details

Authors and affiliations

J. V. Leyendekkers
The University of Sydney, 2006 Australia

A. G. Shannon
Warrane College, The University of New South Wales, 1465,
& KvB Institute of Technology, North Sydney, 2060, Australia

Abstract

The squares of primes in the Modular Ring fall in even rows, , in Class with and (depending on the parity of ). The values are found to equal the rows that the primes occupy when is set as a tabular array. The primes in equal a unique sum or difference of squares and via , the pairs can be identified within the  structure. The n values for composites follow well-defined linear functions that permit easy sorting. Finally, the parameter in the well-known function has been identified as the row in one or more of the Modular Rings or that contains one or more primes.

AMS Classification

• 11A07
• 11A41

References

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